Large language models (LLMs) are increasingly utilized in healthcare applications. However, their deployment in clinical practice raises significant safety concerns, including the potential spread of harmful information. This study systematically assesses the vulnerabilities of seven LLMs to three advanced black-box jailbreaking techniques within medical contexts. To quantify the effectiveness of these techniques, we propose an automated and domain-adapted agentic evaluation pipeline. Experiment results indicate that leading commercial and open-source LLMs are highly vulnerable to medical jailbreaking attacks. To bolster model safety and reliability, we further investigate the effectiveness of Continual Fine-Tuning (CFT) in defending against medical adversarial attacks. Our findings underscore the necessity for evolving attack methods evaluation, domain-specific safety alignment, and LLM safety-utility balancing. This research offers actionable insights for advancing the safety and reliability of AI clinicians, contributing to ethical and effective AI deployment in healthcare.